Problem: Solve for $x$ and $y$ using substitution. ${-4x-6y = 10}$ ${y = 2x+9}$
Answer: Since $y$ has already been solved for, substitute $2x+9$ for $y$ in the first equation. ${-4x - 6}{(2x+9)}{= 10}$ Simplify and solve for $x$ $-4x-12x - 54 = 10$ $-16x-54 = 10$ $-16x-54{+54} = 10{+54}$ $-16x = 64$ $\dfrac{-16x}{{-16}} = \dfrac{64}{{-16}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = 2x+9}\thinspace$ to find $y$ ${y = 2}{(-4)}{ + 9}$ $y = -8 + 9$ $y = 1$ You can also plug ${x = -4}$ into $\thinspace {-4x-6y = 10}\thinspace$ and get the same answer for $y$ : ${-4}{(-4)}{ - 6y = 10}$ ${y = 1}$